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Attempt either (a) or (b) :
(a) A smart home uses energy monitoring system to track electricity usage of appliances. In a month of 30 days, the following devices are used:
1. An electric heater of $1500\ \text{W}$ used for 4 hours daily.
2. A microwave oven rated at $1.5\ \text{kW}$ used for 3 hours daily.
(i) Define electric power and write its SI unit.
(ii) Calculate the total energy consumed in joules and $\text{kWh}$ in a whole month.
(iii) Find out the total cost of electricity for running both appliances for a month of 30 days if the cost of 1 unit is ₹7.
(a) A smart home uses energy monitoring system to track electricity usage of appliances. In a month of 30 days, the following devices are used:
1. An electric heater of $1500\ \text{W}$ used for 4 hours daily.
2. A microwave oven rated at $1.5\ \text{kW}$ used for 3 hours daily.
(i) Define electric power and write its SI unit.
(ii) Calculate the total energy consumed in joules and $\text{kWh}$ in a whole month.
(iii) Find out the total cost of electricity for running both appliances for a month of 30 days if the cost of 1 unit is ₹7.
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(a)
(i)
$\bullet$ Electric power is defined as the rate at which electrical energy is
consumed in an electric circuit. (1)
$\bullet$ S.I unit is watt. ($\frac{1}{2}$)
(ii) Electrical energy consumed=Power$\times$ time
Electrical energy consumed by heater in 1 day
$\text{E=1500}\times\text{4=6000Wh=6kWh}$
Electrical energy consumed by heater in 30days=6$\times$30=180kWh ($\frac{1}{2}$)
Electrical energy consumed by oven in 1 day=1.5$\times$3=4.5kWh
Electrical energy consumed by oven in 30 days=4.5$\times$30=135kWh ($\frac{1}{2}$)
Total energy consumed in whole month=180+135=315kWh ($\frac{1}{2}$)
Total energy consumed in joules=315$\times 3.6 \times 10^6 = 1134 \times 10^6 \text{J}$ ($\frac{1}{2}$)
(iii)Total cost =Total energy consumed $\times$ Cost of 1 unit
=315$\times$7= Rs.2205 (1)
(i)
$\bullet$ Electric power is defined as the rate at which electrical energy is
consumed in an electric circuit. (1)
$\bullet$ S.I unit is watt. ($\frac{1}{2}$)
(ii) Electrical energy consumed=Power$\times$ time
Electrical energy consumed by heater in 1 day
$\text{E=1500}\times\text{4=6000Wh=6kWh}$
Electrical energy consumed by heater in 30days=6$\times$30=180kWh ($\frac{1}{2}$)
Electrical energy consumed by oven in 1 day=1.5$\times$3=4.5kWh
Electrical energy consumed by oven in 30 days=4.5$\times$30=135kWh ($\frac{1}{2}$)
Total energy consumed in whole month=180+135=315kWh ($\frac{1}{2}$)
Total energy consumed in joules=315$\times 3.6 \times 10^6 = 1134 \times 10^6 \text{J}$ ($\frac{1}{2}$)
(iii)Total cost =Total energy consumed $\times$ Cost of 1 unit
=315$\times$7= Rs.2205 (1)